Change Point Analysis of the Time to Recurrence in Colon Cancer Patients

Change point analysis is essential in the identification of shifts in disease progression, particularly in assessing recurrence risk in cancer patients. This study evaluated whether the likelihood of colon cancer recurrence remains constant over time or changes across time. The Likelihood Ratio Test (LRT) was applied to detect significant changes in the hazard function, and maximum likelihood estimation was used to estimate the change points. A bootstrap resampling scheme generated the empirical distribution of the LRT statistic under the null hypothesis of no change. Simulation studies assessed the power of the LRT, showing improved accuracy with increased sample size, larger hazard differences, and centrally located change points. The proposed method was applied to a real colon cancer dataset comprising 888 patients, of whom 446 experienced recurrence. Four covariates—treatment type, number of positive nodes, extent of local spread, and time to registration—were found to be significant and were included in the change point detection analysis. Each covariate showed one significant change point based on the LRT exceeding the bootstrap critical value. In the Cox Proportional Hazards model, treatment was associated with a greater reduction in hazard after the change point, while the other covariates were associated with increased recurrence risk, with stronger effects post-change. In the Weibull Accelerated Failure Time (AFT) model, treatment was associated with a reduced hazard, while the covariates linked to increased hazard exhibited slightly weaker effects after the change. Model adequacy was evaluated using Cox–Snell and deviance residuals, Schoenfeld residuals, quantile–quantile plots, and the Grambsch–Therneau test. Models with change points performed better across all checks, except the Weibull AFT model, which failed the quantile– quantile plot test. Overall, the Cox Proportional Hazards model with covariate-specific change points provided the best fit, offering critical insight into dynamic recurrence risk patterns in colon cancer patients. These findings provide a basis for cancer surveillance agencies and public health organizations to refine screening programs and allocate resources efficiently by focusing on high-risk periods.